The prime minister's third overnight stay in St Thomas' Hospital's ICU was "good", and he is "in good spirits", the spokesperson added.
The PM continues to receive oxygen treatment for Covid-19, there's "no change to that", he added.
He said Mr Johnson is still "not working" and has asked Dominic Raab to "deputise for him" and "lead any Cabinet decision making process".
One key decision due to be made next week is whether to relax lockdown restrictions, but Downing Street has hinted that will not happen.
- ITV News Political Correspondent Libby Wiener reports on the latest statement from Downing Street:
The government is due to carry out the first review next week of the lockdown measures announced last month to curb the spread of the disease.
However, the Prime Minister’s official spokesman did not contradict a warning by Scottish First Minister Nicola Sturgeon that there was no possibility of any relaxation of the restrictions at that point.
“What we absolutely need to do now is keep bearing down on the rate of transmission which will mean continuing with social distancing measures to ensure we are protecting the NHS and saving lives,” the spokesman said.
“We are at a critical point in this. That is certainly the case as we approach the Easter bank holiday weekend.”
Culture Secretary Oliver Dowden earlier gave an update on the Prime Minister’s health, saying Mr Johnson is doing “reasonably well” in the London hospital.
Asked about whether the PM will be able to make a decision himself on the lockdown next week, Mr Dowden told BBC Radio 4’s Today programme: “He’s in a stable condition, he seems to be doing reasonably well, he was sat up and engaging with medical staff.
“But we have a well-established mechanism for the first minister Dominic Raab to take the Prime Minister’s place in chairing such meetings, he will chair Cobra and he will chair the relevant decisions.
"This is just about going through a proper process, that’s why we’re waiting for next week.”
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